Average Error: 31.7 → 0.0
Time: 1.2s
Precision: 64
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\mathsf{hypot}\left(re, im\right)\]
\sqrt{re \cdot re + im \cdot im}
↓
\mathsf{hypot}\left(re, im\right)
double f(double re, double im) {
        double r910110 = re;
        double r910111 = r910110 * r910110;
        double r910112 = im;
        double r910113 = r910112 * r910112;
        double r910114 = r910111 + r910113;
        double r910115 = sqrt(r910114);
        return r910115;
}
↓
double f(double re, double im) {
        double r910116 = re;
        double r910117 = im;
        double r910118 = hypot(r910116, r910117);
        return r910118;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 31.7

    \[\sqrt{re \cdot re + im \cdot im}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{hypot}\left(re, im\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{hypot}\left(re, im\right)\]

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))